This section is intended to introduce various aspects of the art, which may be associated with aspects of the disclosed techniques and methodologies. A list of references is provided at the end of this section and may be referred to hereinafter. This discussion, including the references, is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the disclosure. Accordingly, this section should be read in this light and not necessarily as admissions of prior art.
Extensional strain in the brittle crust of the earth is usually accommodated by opening mode natural fractures, known as joints that grow perpendicular to the most tensile principal stress. Joints can form under a combination of macromechanically driven loading conditions, such as elevated pore pressures, folding of geological strata, vertical stacking of heterogeneous layers, slip along preexisting faults, and others. Although the existence of microflaws may play a role in fracture initiation and propagation, mechanically driven factors dominate the resulting natural fracture patterns. Natural fractures occur in varying orientations, occur in clusters, have different propagating lengths and have various apertures. One of the main tasks of fracture prediction is to be able to characterize such properties.
Because joints may affect the movement, storage and recovery of hydrocarbons, a substantial effort has been focused on predicting the characteristics of subsurface systems. The most commonly sought characteristics include the intensity, aperture and orientation of the dominant set of joints. In data rich fields, fracture characterization efforts include analyzing the image log and core data, and sometimes investigating seismic attributes such as the azimuthal variation of P-wave velocities or amplitude vs offset (Keating and Fischer (2008)). However, in fields where subsurface data are limited, or in the early stages of exploration, fracture characteristics are usually predicted from 2D or 3D restoration or curvature analyses which have limited power for fracture prediction.
From a computational point of view, historically pure continuum models have been favored over discontinuum models for modeling naturally occurring fractures. This is due to their computational efficiency and ease of implementation. However, continuum models are unable to realize true material separation, ultimately exhibiting regions of zero strength and effectively eliminating meaningful post failure interaction, which may include predicting multiple sets of fractures. Indeed, all fracture in quasi-brittle materials is associated with extension and parting of material planes. In this sense, the principal problem with continuum models is that the resultant models are “too stiff” when no a priori knowledge of crack initiation or distribution is available. To develop computational methodologies with truly predictive capabilities, emphasis must be placed on the evolution of material response throughout the deformation process.
Currently such evolving material response is homogenized and is represented using phenomenological models. Given that discontinuities in rocks manifest with deformation and perturb the stress field (i.e. by introducing stress concentrations and additional kinematic freedom), accurate representation of their influence within computational models can be achieved only when the continuum models evolve naturally into a discontinuum model.
Although modeling fractures in rock masses may be of practical importance, this problem is among the most difficult to solve because fracture state evolves continuously and is not known a priori. At any time during the deformation process, fractures may be open, partly or completely closed and, if open, may close under compression. Furthermore, parts of closed fractures may begin to slip and later stick and initiate additional discrete fracture sets such as splaying or wing fractures. Thus, any numerical approach that aims to predict fracture characteristics (such as length, aperture and intensity) should be able to capture the sequential evolution of discontinuities within a model, preferably starting from a continuum state without a prior knowledge of the microflaw distribution. What is needed is a novel methodology that predicts naturally occurring fractures and damage in subsurface regions.
Broadly speaking, six different techniques have been used to predict occurrence of natural fractures and associated damage in a subsurface region: analytical methods, curvature analysis, restoration analysis, stochastic techniques, continuum mechanical models and other mechanical methods. Each of these techniques will now be discussed.
Analytical Methods: The use of analytical methods based on linear elastic fracture mechanics for fracture prediction (due to single or multiple preexisting fractures) (Horii and Nemat-Nasser (1986)) is difficult and arduous (Schlangen and Garboczi (1997)). The analytical models simplify geological processes such as boundary & loading conditions, material heterogeneity, geometry, interface friction, and post fracture interaction. Thus in most cases the analytical models overlook important factors that control primary fracture characteristics such as spacing and length (Ladeira and Price (1981); Ji et. al. (1998a); Ji et al (1998b); Timm et al. 2003)). For example, none of the aforementioned analytical techniques can take into account post fracture interaction, sequential fracturing, advanced constitutive models, material failure and complex layering. Furthermore, most of these solutions are derived under absolute tension which is rarely the case in nature. The most promising application of analytical solutions to natural fracture prediction comes from Eidelman et al. (1992) and Reches (1998) who analyzed the stress state and fracturing within stiff elliptical inclusions and brittle flat lying layers embedded in more compliant matrix (such as shale or poorly consolidated conglomerates) using Eshelby's analytical solution (Eshelby (1957)). The conclusion was that tensile fracturing might occur due to stress amplification associated with the stiffness contrast between the weak matrix and stiff inclusion(s)/layer(s). However, this approach also suffers from the limitations of the aforementioned analytical solutions: it has limited predictive power for identifying natural fracture characteristics such as intensity, spacing and connectivity and damage localization.
Curvature Analysis: In curvature analysis, it is assumed that layers of rocks deform like elastic plates. A mechanical analysis of such bending plates suggests that layer-parallel strains are directly related to the curvature of the folded surface (Fischer and Wilkerson, 2000). As summarized in Keating and Fischer (2008), a variety of methods of curvature analysis for fracture prediction have been proposed and tested (Schultz-Ela et al. (1992); Ericsson et al. (1998); Roberts (2001); Bergbauer and Pollard (2003); Bergbauer and Pollard (2004); Pearce et al. (2006)). Such tests typically compare curvature-based predictions of fracture intensity or orientation with core data, image logs, or production data from well-developed fields (Keating and Fischer (2008). The results of these tests are inconsistent. In some cases curvature analysis seems to agree with field observations (Lisle (1994); Ericsson et al. (1998)), however in other cases they yield completely opposite results (Silliphant et al. (2002); Allwardt et al. (2007)). The major limitations of curvature analysis can be listed as follows:                1. Folding/bending is not the only mechanism that may cause fracturing;        2. Continued extension might be accommodated by the reactivation of existing fractures (either shear or opening) instead of forming new fractures (Nan (1991); Bergbauer and Pollard (2004));        3. Curvature is not always a direct measure for strain or fracture intensity (Keating and Fischer. (2008));        4. Curvature analysis on the present day geometry does not consider geological history and might significantly underestimate the total deformation throughout geological time (Sanders et al. (2004)).Therefore, unless additional kinematic and mechanical constraints are introduced, curvature based fracture predictions remain problematic.        
Restoration Analysis: Restoration analysis methods for natural fracture prediction fall into two major categories:
1. Geometric and kinematic
2. Mechanical
Geometric and kinematic analysis cover most commonly used restoration techniques that aim at reproducing natural deformation patterns including faults and fractures. This analysis assumes areas that accommodate large strains might be associated with faulting and fracturing. Maerten and Maerten (2006) provide an extended review of these techniques that include: balancing cross sections by flexural slip (Dahlstrom (1969)); vertical or inclined shear techniques (Williams and Van (1987); White et al. (1986); Dula (1991)); geometric unfolding methods for 3D surfaces (Gratier et al. (1991); (Kerr et al. (1993); Williams et al. (1997)); map view restoration using rigid translation and rotation of fault blocks (Rouby et al. (1993)).
The restoration techniques mentioned above are inadequate due to the following reasons: it is uncertain which geometric restoration algorithm should be used to model rock deformation (Hauge and Gray (1996); Bulnes and McClay (1999); Maerten and Maerten (2006)); they are not based on the fundamental principles of the conservation of mass; no rock mechanical properties are incorporated in the models; mechanical interaction among faults and fractures is not considered; and only strain rather than stress is calculated as a proxy for fracture predictions. (Hennings et al. (2000); Rouby et al. (2000); Sanders et al. (2004)).
Maerten and Maerten (2006) showed that adding geomechanics to restoration techniques leads to more realistic predictions of fracture patterns: mechanical restorations incorporate fundamental physical laws that govern fracture initiation and propagation. Although mechanical restorations provide a significant uplift compared to geometric and kinematic restorations, fracture predictions are usually diffuse because they use a continuum approach with no failure. As a summary the major pitfalls of mechanical restoration analysis can be listed as follows: fracture predictions are limited to continuum-elastic analyses (i.e. no tensile failure criterion is implemented) thus leading to unrealistic stress concentrations and diffuse deformations and the analyses are only applicable to folded and faulted regions.
Stochastic Techniques: Stochastic techniques, as summarized in Walsh and Watterson (1991); Schlische et al. (1996)) and Maerten and Maerten (2006), are based on the fracture power-law size distributions and usually calibrated using available field data Although the size distributions are predictable, these techniques pay little or no consideration to physical concepts that govern fault and fracture development. Consequently they cannot take advantage of the constraints imposed by physical laws to predict the orientations and the location of these geological features (Maerten and Maerten (2006)). This becomes especially problematic when fractures are populated using statistical rules that are based on limited or poor field data. Thus mechanical considerations for joint termination, length, saturation limits and others are simply ignored. Predictions solely depend on a combination of experience, available in-situ fracture data and statistical assumptions, hence limiting the predictive capabilities of this approach significantly.
Continuum Mechanical Analysis: In classical finite element modeling (FEM), emphasis is given to the continuum response of the subsurface region. That is, in a problem domain, the materials cannot fracture (i.e. open) or be broken into pieces. Therefore fragmentation and rigid body motion is ignored. In this sense a continuous system reflects mainly the “material deformation” rather than movement, kinematics, fracture opening and interaction. A number of large scale (i.e. 2D and 3D) attempts to use a continuum damage approach have been made for predicting naturally occurring faults and fractures. These include Leroy and Sassi (2000), Beekman et al. (2000), Guiton et al. (2003a-b), and Alvarez-Gomez et al. (2008). These models stay qualitative because of the limitations of large scale models and continuum approximation of fracture occurrence. In these simulations failure is associated with plastic deformation. In other words, localized plastic strain indicates brittle faulting and less intense or more diffuse distribution of the plastic deformation would be a proxy for fractures. This approach is not entirely correct for Mode-I brittle failure where fractures initiate predominantly under tension rather than shear. To summarize the major limitations of current continuum modeling attempts for natural fracture prediction: (a) continuum models do not allow modeling of individual fractures; (b) continuum models are better suited for predicting shear localization or activation of preexisting discontinuities rather than initiation of Mode-I, opening type deformation; (c) the possibility of post failure fracture interaction and coalescence is ignored, thus prediction of multiple sets is difficult or rather erroneous; and (d) all natural fracturing in quasi-brittle rock is associated with extensional deformation and parting of material planes. Previous attempts in this area suggest damage and fracturing initiate in opening Mode-I and then coalesce to form slip surfaces or so-called shear fractures.
Mechanical Methods: There are other mechanical methods such as Distinct Element Method, XFEM (extended finite element), DDM (Displacement Discontinuity Method), and spring lattice networks, with potential applications to natural fracture prediction. The current limitation of Distinct Element based codes for natural fracture simulations is related to the high number of particles necessary for discretization even for small-scale problems. Another limitation is that particle interaction and fracture propagation—and thus the overall deformation—is controlled by spring stiffness. In other words, fracture propagation is assigned to the boundaries of the particles that are initially in contact. When the bonds between contacting particles react to the applied stress or strains and break, or if the stress state dictates that they should, fractures initiate and propagate. However, spring constants cannot be extracted directly from conventional lab tests: they are scale dependent and remain artificial parameters without extensive calibration against experimental observations.
The DDM requires the discretization of only the preexisting discontinuities (Crouch and Starfield (1983)), thus reducing the computational time significantly. DDM is most suitable for fracture propagation simulations due to slip or openings along preexisting fractures, and thus a priori knowledge of large scale faults or microscale flaws is required. This limits the applicability of this tool for naturally occurring fractures where a number of different geologically plausible scenarios exist. In most DDM based simulations, natural fractures propagate from the tips of preexisting discontinuities once a critical stress intensity is reached, putting the emphasis on microscale damage. This creates another challenge for analyzing fracturing process using DDM: what happens in the fracture tips in rocks still remains to be adequately understood. Therefore, simulations should not depend solely on micromechanics of the failure.
There are no known current applications of large-scale or small-scale XFEM for natural fracture prediction. Known XFEM methods can incorporate cohesive element technology and a variety of fracture initiation and propagation criteria. However, most applications of XFEM focus on dynamic or hydraulic fracture propagation with specific focus on microscale initiation mechanisms such as crack tip process zone and crack tip plasticity. Thus applications are limited to simulation of a single or few large fractures.
The combination of statistical theory with numerical models such as the lattice model (Van Mier (1997)) are found to be appropriate for modeling brittle rock behavior. However, at present lattice models do not seem well suited for modeling compressive rock failure. U.S. Pat. No. 6,370,491 and U.S. Pat. No. 7,043,310, both having inventors Malthe-Sorenssen et al., describe such a lattice network model that incorporates beam or spring elements. In lattice networks material properties assigned to beam elements include elastic coefficients and a breaking strength. Spring elements are modeled with artificial spring constants and a breaking length. In general this application suffers from the same pitfalls of earlier lattice models. The model as described in these two patents has several limitations. First, the lattice model does not incorporate advanced constitutive models and plastic deformation. Second, the model simulates fractures due to opening along a predefined plane of weaknesses under local tension. However, this is rarely the case in nature where in most cases rock is subjected to overall compression. The issues of (i) fracture propagation under overall compression, (ii) fracture propagation under biaxial tension and compression, and (iii) mechanically driven natural fracture formation due to elevated pore pressures, vertical stacking of heterolithic rocks, folding, and/or slip along preexisting faults, are not addressed explicitly. Third, the model does not incorporate discrete layering and contact along newly created fracture surfaces. That is, contact normal and shear stresses are not taken into account along layer interfaces or newly created discontinuities. In other words, fractures remain open as broken bonds remain repulsive. This is an oversimplification of natural processes. Indeed, natural fractures might close under compression and establish contact. Once a critical shear stress is reached, slip occurs and new sets of fractures are created in the form of wing cracks. Without well-established contact and friction algorithms, applications are strictly limited to extensional settings. Fourth, the model incorporates only breaking strength or length. However, quasi-brittle materials are better characterized by the transition between the strength based failure criteria and energy based criteria of LEFM (i.e. linear elastic fracture mechanics). Natural fracture prediction requires a combination of strength and energy release rate that defines the post peak behavior. Fifth, large scale faults are pre-defined in a spring lattice model. In nature, however, faulting and fracturing occur simultaneously. That is, small scale fractures coalesce and form large scale faults. Likewise, fault propagation might also promote fractures in the vicinity of fault tips. A method with predictive capabilities therefore should minimize human interaction and let the stress state dictate fracturing, faulting and the feedback they provide for each other. Sixth, the method does not address post fracture interaction and fracture saturation. Also, it is not stated explicitly whether fracture characteristics such as aperture, length, intensity, and spacing could be obtained routinely from the simulations. Lastly, elastic constants used in the spring lattice models are not based on experimental results and remain artificial parameters.
Existing methods are not suitable for predicting fracture occurrence under general loading and boundary conditions. There is a need for an invention that is able to predict natural fracturing and damage on a variety of scales/scenarios in a subsurface region. Such an invention should preferably take into account more realistic elastic and plastic rock properties, mechanical layering, contact detection algorithms and friction, fracture mechanics parameters such as energy release rates and/or critical stress intensity, complex boundary conditions and model geometry, and integrate preexisting fracture prediction tools. There is a need for a robust approach that would simulate fracturing and damage due to a variety of geologically plausible conditions and loading regimes, both in extension and compression. Such a solution should benefit from the advantages of current natural fracture prediction tools and integrate them in a single/simple workflow. Also, the solution should be applicable to cases where limited or no a priori preconditioning is available, for example preexisting discontinuities and/or micro-flaws, therefore minimizing human interaction. Furthermore, fracture characteristics such as length, spacing, aperture, connectivity and intensity should be obtained routinely from the numerical analysis.
A recently new technique FEM-DEM can simulate transition of rock from a state of continuum to discontinuum. An extended review of FEM-DEM and computational aspects can be found in Munjiza (2004). FEM-DEM has been primarily applied in defense industry, civil and mining engineering where excessive fragmentation occurs and large material regions fail simultaneously. Due to the nature of unstable propagation and simultaneous failure in these settings, discrete fracture characteristics such as spacing and intensity can no longer be extracted from such models. In contrast, natural fractures (i.e. under overall compression under gravity and tectonic loading conditions) may propagate very slowly and stably. In this sense simulations based on FEM-DEM can be used to extract the key characteristics of natural fractures.
Various applications of FEM-DEM include fractures due to blasting (Wei et al. (2007)) and fractures due to underground excavations and experimental rock mechanics problems (Klerck (2000); Sellers and Klerck (2000); and Klerck et al (2004)). Other engineering applications cover wellbore breakout (Crook et al. (2003)) and rock slope instability (Stead and Coggan (2006)), Eberhardt et al. (2004)).